Average Error: 28.2 → 0.2
Time: 7.2s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \left(z + x\right) \cdot \frac{x - z}{y}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \left(z + x\right) \cdot \frac{x - z}{y}}{2}
double f(double x, double y, double z) {
        double r1310604 = x;
        double r1310605 = r1310604 * r1310604;
        double r1310606 = y;
        double r1310607 = r1310606 * r1310606;
        double r1310608 = r1310605 + r1310607;
        double r1310609 = z;
        double r1310610 = r1310609 * r1310609;
        double r1310611 = r1310608 - r1310610;
        double r1310612 = 2.0;
        double r1310613 = r1310606 * r1310612;
        double r1310614 = r1310611 / r1310613;
        return r1310614;
}
↓
double f(double x, double y, double z) {
        double r1310615 = y;
        double r1310616 = z;
        double r1310617 = x;
        double r1310618 = r1310616 + r1310617;
        double r1310619 = r1310617 - r1310616;
        double r1310620 = r1310619 / r1310615;
        double r1310621 = r1310618 * r1310620;
        double r1310622 = r1310615 + r1310621;
        double r1310623 = 2.0;
        double r1310624 = r1310622 / r1310623;
        return r1310624;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original28.2
Target0.2
Herbie0.2
\[y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right)\]

Derivation

  1. Initial program 28.2

    \[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]

  2. Simplified12.7

    \[\leadsto \color{blue}{\frac{y + \frac{x \cdot x - z \cdot z}{y}}{2}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity12.7

    \[\leadsto \frac{y + \frac{x \cdot x - z \cdot z}{\color{blue}{1 \cdot y}}}{2}\]

  5. Applied difference-of-squares12.7

    \[\leadsto \frac{y + \frac{\color{blue}{\left(x + z\right) \cdot \left(x - z\right)}}{1 \cdot y}}{2}\]

  6. Applied times-frac0.2

    \[\leadsto \frac{y + \color{blue}{\frac{x + z}{1} \cdot \frac{x - z}{y}}}{2}\]

  7. Simplified0.2

    \[\leadsto \frac{y + \color{blue}{\left(z + x\right)} \cdot \frac{x - z}{y}}{2}\]

  8. Final simplification0.2

    \[\leadsto \frac{y + \left(z + x\right) \cdot \frac{x - z}{y}}{2}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"
  :precision binary64

  :herbie-target
  (- (* y 0.5) (* (* (/ 0.5 y) (+ z x)) (- z x)))

  (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)))